Proton current conservation equation

The aforementioned models include three governing equations (i) mass transport equation for oxygen, (ii) proton current conservation equation with the Tafel rate of electrochemical reaction on the right side and (iii) Ohm s law, which relates proton current to the gradient of overpotential. Due to the exponential dependence of the rate of ORR on overpotential this system is strongly non-linear. 

To illustrate the use of the Tafel equation, consider the following simple problem. Let the proton current density jo enter the cathode catalyst layer from the membrane. In the CCL, this current is converted into the electron current and at the CCL/GDL interface the proton current = 0. The proton current conservation equation reads... 

Equation 4.226 is a proton current conservation equation. The right side of Equation 4.226 is a rate of proton production (A cm ) in the ACL given by... 

These potentials are governed by proton and electron current conservation equations ... 

Equation 5.129 describes the proton current conservation protons are consumed in the ORR (the first term on the right side), produced in the MOR (the second term), and charge the double layer (the first term on the left side). Equations (5.130) and (5.131)... 

Using the simple model psd in Eq. (2.79) and the assumption of fast proton transport, a full solution of the system of conservation equations in Section 2.6 could be found, providing the pressure distributions p z), q z),p z), the capillary pressure p z) = p z) + q z) + p — p z), the current density distribution j z), and the overall relation between overpotential and total current density, r o(/b)- This solution highlights several vital functions of CCLs for the fuel cell water balance. 

Consider for definiteness the cathode catalyst layer. Proton current density jp obeys a conservation equation djpjdx = -Q. Using this relation in (1.64) we get... 

Equation 5.80 describes charge conservation in the CCL. It shows that the proton current decays toward the GDL because of the charging of the double layer (the term with Cdl) and due to the proton conversion in the ORR (the right side of this equation). Equation 5.80 follows from a general charge conservation equation... 

Under conditions of constant current, namely, under steady-state operation, reactants must be supplied continuously and at a constant rate to precisely balance the rate of reactant consumption in electrode reactions. The coupled fluxes of electrons, protons, and gaseous reactants are subdued to two fundamental conservation laws, which complete the description of the fuel cell principle conservation of charge and mass. These laws allow balance or continuity equations to be written among all involved... 

Although Faraday s results were purely experimental, the important implication from this proportional relationship was that electrical current was a result of discrete particles we now understand to be ions and electrons that are conserved as part of an overall balanced reaction equation. This understanding enabled quantification of many electrical phenomena and helped reveal the nature of protons and electrons. 

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